well the cap MAY help in the dimming of headlights, but like explained by op, it literally killing his battery. do you really think even a 20-30 farad capacitor will clear up an issue as bad as this? also, as crazy as it sounds, he wants to add Multiple 2000w amps, with just a cap.
I am doubtful a cap will fix this issue.(why spend all this money on 3-4 caps, when you can gnerally get a decent ho alternator for 300$) if this were the case, then why don't you see caps in competition vehicles for spl? generally you see a huge bank of batteries, and i can guarantee an HO alternator. IF it were that simple, then everyone would just skip the HO's and the multiple batteries and get banks of caps, which i am sure only an idiot would do.
but if you like the smell of burnt mosfets, then go ahead, keep running your amp at 10 volts until your car stalls.